311 (number)

← 310 311 312 →
List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	three hundred eleven
Ordinal	311th (three hundred and eleventh)
Factorization	311
Prime	twin prime
Roman numeral	CCCXI
Binary	1001101112
Ternary	1021123
Quaternary	103134
Quinary	22215
Senary	12356
Octal	4678
Duodecimal	21B12
Hexadecimal	13716
Vigesimal	FB20
Base 36	8N36
Hebrew	שיא

311 is the natural number after 310 and before 312.

In mathematics

311 is a twin prime with 313; an irregular prime;^[1] an Eisenstein prime with no imaginary part and real part of the form $3n-1$; a Gaussian prime with no imaginary part and real part of the form $4n-1$; and a permutable prime with 113 and 131.

It can be expressed as a sum of consecutive primes in four different ways: as a sum of three consecutive primes (101 + 103 + 107), as a sum of five consecutive primes (53 + 59 + 61 + 67 + 71), as a sum of seven consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59), and as a sum of eleven consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

311 is a strictly non-palindromic number, as it is not palindromic in any base between base 2 and base 309.^[2]

Notable uses of numerical value

• 311 is used in the name of a gang in Las Vegas, known as the 311 Boyz.
• 311 was formerly the Los Angeles Police Code for an armed robbery. This is sometimes referenced in Hip-Hop/Rap music and films.
• 3-1-1 is a special phone number used in many large cities such as New York City, Chicago, Houston, and Los Angeles that provides access to non-emergency municipal services.
• 311 is the name of an American alternative rock band.
• As "311" or "3/11", typically pronounced "three-eleven" by analogy with "9/11", it is commonly used to refer the calendar dates November 3 or March 11, depending on which date notation is used. The latter usage may refer to the March 11, 2011, Tōhoku earthquake and tsunami in Japan or the March 11, 2004, Madrid train bombings.
• According to some people 311 stands for KKK because K is the 11th letter of the alphabet (Three 11s = Three Ks = KKK)^[3]

References

1. "Sloane's A000928 : Irregular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
2. "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
3. Hate Number Symbols: 311 - From A Visual Database of Extremist Symbols, Logos and Tattoos. Anti-Defamation League. Accessed 2008-08-21. "The eleventh letter of the alphabet is the letter "K"; thus 3 times 11 equals "KKK," or Ku Klux Klan."